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Over-parameterized deep neural networks are able to achieve excellent training accuracy while maintaining a small generalization error. It has also been found that they are able to fit arbitrary labels, and this behaviour is referred to as…

Machine Learning · Computer Science 2021-12-17 Futong Liu , Tao Lin , Martin Jaggi

The generalization mystery in deep learning is the following: Why do over-parameterized neural networks trained with gradient descent (GD) generalize well on real datasets even though they are capable of fitting random datasets of…

Machine Learning · Computer Science 2022-06-07 Satrajit Chatterjee , Piotr Zielinski

Understanding the generalization behaviour of deep neural networks is a topic of recent interest that has driven the production of many studies, notably the development and evaluation of generalization "explainability" measures that…

Machine Learning · Computer Science 2021-10-26 Jonathan Jaegerman , Khalil Damouni , Mahdi S. Hosseini , Konstantinos N. Plataniotis

State-of-the-art pre-trained language models have been shown to memorise facts and perform well with limited amounts of training data. To gain a better understanding of how these models learn, we study their generalisation and memorisation…

Computation and Language · Computer Science 2022-03-16 Michael Tänzer , Sebastian Ruder , Marek Rei

Diffusion models excel at generating high-quality, diverse samples, yet they risk memorizing training data when overfit to the training objective. We analyze the distinctions between memorization and generalization in diffusion models…

Machine Learning · Computer Science 2026-02-12 Zekai Zhang , Xiao Li , Xiang Li , Lianghe Shi , Meng Wu , Molei Tao , Qing Qu

State of the art deep generative networks are capable of producing images with such incredible realism that they can be suspected of memorizing training images. It is why it is not uncommon to include visualizations of training set nearest…

Machine Learning · Computer Science 2019-01-14 Ryan Webster , Julien Rabin , Loic Simon , Frederic Jurie

Despite their massive size, successful deep artificial neural networks can exhibit a remarkably small difference between training and test performance. Conventional wisdom attributes small generalization error either to properties of the…

Machine Learning · Computer Science 2017-02-28 Chiyuan Zhang , Samy Bengio , Moritz Hardt , Benjamin Recht , Oriol Vinyals

We propose a method, called Label Embedding Network, which can learn label representation (label embedding) during the training process of deep networks. With the proposed method, the label embedding is adaptively and automatically learned…

Machine Learning · Computer Science 2017-10-31 Xu Sun , Bingzhen Wei , Xuancheng Ren , Shuming Ma

Along with the rapid development of deep learning in practice, the theoretical explanations for its success become urgent. Generalization and expressivity are two widely used measurements to quantify theoretical behaviors of deep learning.…

Machine Learning · Computer Science 2018-03-26 Shao-Bo Lin

We study the memorization and generalization capabilities of Diffusion Models (DMs) when data lies on a structured latent manifold. Specifically, we consider a set of $P$ data points in $N$ dimensions confined to a latent subspace of…

Disordered Systems and Neural Networks · Physics 2025-05-27 Beatrice Achilli , Luca Ambrogioni , Carlo Lucibello , Marc Mézard , Enrico Ventura

The impressive capabilities of large language models (LLMs) have sparked debate over whether these models genuinely generalize to unseen tasks or predominantly rely on memorizing vast amounts of pretraining data. To explore this issue, we…

Computation and Language · Computer Science 2025-03-04 Xinyi Wang , Antonis Antoniades , Yanai Elazar , Alfonso Amayuelas , Alon Albalak , Kexun Zhang , William Yang Wang

Grokking is the intriguing phenomenon where a model learns to generalize long after it has fit the training data. We show both analytically and numerically that grokking can surprisingly occur in linear networks performing linear tasks in a…

Machine Learning · Statistics 2024-02-06 Noam Levi , Alon Beck , Yohai Bar-Sinai

Rote learning is a memorization technique based on repetition. Many researchers argue that rote learning hinders generalization because it encourages verbatim memorization rather than deeper understanding. This concern extends even to…

Computation and Language · Computer Science 2026-03-03 Qinyuan Wu , Soumi Das , Mahsa Amani , Bishwamittra Ghosh , Mohammad Aflah Khan , Krishna P. Gummadi , Muhammad Bilal Zafar

We study the interplay between memorization and generalization of overparameterized networks in the extreme case of a single training example and an identity-mapping task. We examine fully-connected and convolutional networks (FCN and CNN),…

Machine Learning · Statistics 2020-01-10 Chiyuan Zhang , Samy Bengio , Moritz Hardt , Michael C. Mozer , Yoram Singer

Recent research on the grokking phenomenon has illuminated the intricacies of neural networks' training dynamics and their generalization behaviors. Grokking refers to a sharp rise of the network's generalization accuracy on the test set,…

Machine Learning · Computer Science 2024-05-31 Simin Fan , Razvan Pascanu , Martin Jaggi

We examine the role of memorization in deep learning, drawing connections to capacity, generalization, and adversarial robustness. While deep networks are capable of memorizing noise data, our results suggest that they tend to prioritize…

Background: Deep learning models are typically trained using stochastic gradient descent or one of its variants. These methods update the weights using their gradient, estimated from a small fraction of the training data. It has been…

Machine Learning · Statistics 2018-01-03 Elad Hoffer , Itay Hubara , Daniel Soudry

Recent efforts at explaining the interplay of memorization and generalization in deep overparametrized networks have posited that neural networks $\textit{memorize}$ "hard" examples in the final few layers of the model. Memorization refers…

Machine Learning · Computer Science 2023-07-20 Pratyush Maini , Michael C. Mozer , Hanie Sedghi , Zachary C. Lipton , J. Zico Kolter , Chiyuan Zhang

Deep learning algorithms are well-known to have a propensity for fitting the training data very well and often fit even outliers and mislabeled data points. Such fitting requires memorization of training data labels, a phenomenon that has…

Machine Learning · Computer Science 2020-08-11 Vitaly Feldman , Chiyuan Zhang

Despite their success in image generation, diffusion models can memorize training data, raising serious privacy and copyright concerns. Although prior work has sought to characterize, detect, and mitigate memorization, the fundamental…

Computer Vision and Pattern Recognition · Computer Science 2025-10-01 Juyeop Kim , Songkuk Kim , Jong-Seok Lee